Anatomy of Pearl and Abrikosov Vortices: A Unified Framework for Core and Screening Physics (Part I)
ORAL
Abstract
We present a systematic study of Abrikosov vortex lines in a bulk superconductor and Pearl vortices in a thin films, encompassing the general case of finite coherence length ξ and finite Pearl length Λ, as well as all limiting cases. We solve the radial Ginzburg-Landau equations using complementary analytic and numerical methods – including short- and long-distance series, shooting, relaxation, variational schemes, and linear algebra methods – to obtain the superfluid amplitude, vector potential, current density, magnetic field, and free energy. We show the vortex free energy can be expressed as Fv∝ln[(Λe/ξe)η(Λ/ξ)], where the short-range cutoff ξe≈0.966ξ characterizes the vortex core size and the long-range cutoff Λe≈1.123Λ captures magnetostatic screening. In the limit Λ/ξ→∞, the function η→1, clearly separating core and screening effects. Finally, we derive approximations for the Gibbs free energy of a vortex pinned by a circular hole in the limit rh<<ξ<<Λ.
*Research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-24-1-0150. Work at Cornell has also been supported by the U.S. Department of Energy, Office of Science, Offices of Nuclear Physics and Advanced Scientific Computing Research under contract DE-AC05-06OR23177. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
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Presenters
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Aliakbar Sepehri
- University of North Dakota